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I have a repeated measures dataset (8 measurements) with three experimental groups (Randomly generated). The dependent variable (Y) is on a continuous scale bounded inferiorly at 0. I am trying to model the effect of the different groups and time on Y. What would be the appropriate model here? -

  • repeated ANOVA is compromised by the non-normal distribution of Y (see histogram - I tried adding a minuscule amount and logging, but still really to no help)
  • Mixed linear models are not bounded inferiorly at 0. Perhaps one of the more advanced non-linear mixed models?
  • Area under the curves for all timepoints stratified by group?
  • Bayesian approaches?

Raw Y Absolute values

Logged YLogged values

Histogram of logged Y enter image description here

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  • $\begingroup$ What was a "minuscule amount"? log of (y + 1e-9) is for example usually a much worse idea than log of (y + 1). More importantly, is zero itself an observed value? $\endgroup$
    – Nick Cox
    yesterday
  • $\begingroup$ Y is indeed an observed value—as time increases, the proportion of actual 0-values increases. Minuscule amount: arbitrarily chosen —.0001 $\endgroup$
    – Misha
    yesterday
  • $\begingroup$ I guess you need to say much more about the underlying science. It sounds as if you have a set-up in which the amount is something is decreasing and in particular it may vanish (or at least become undetectable). If so, you need a model geared to that, although I am not clear what it would be. $\endgroup$
    – Nick Cox
    yesterday
  • $\begingroup$ It is a measurement of a quantity that can vanish — I did fit a Bayesian beta-regression where the posterior predictive check looks reasonable for all measurements - but should the pp-check also be repeated for each time-point? $\endgroup$
    – Misha
    yesterday
  • $\begingroup$ Sorry, can't help at all on Bayesian detail. $\endgroup$
    – Nick Cox
    yesterday

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